Is sin(3u)=sin(u)(3-4sin^2(u)) ?

The answer to whether sin(3u)=sin(u)(3-4sin^2(u)) is True

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prove sin(3u)=sin(u)(3-4sin^2(u))

prove

sin (3 u) = sin (u) (3 - 4 sin^{2} (u))

True

Solution steps

sin (3 u) = sin (u) (3 - 4 sin^{2} (u))

Manipulating left side

sin (3 u)

Rewrite using trig identities

= 3 sin (u) - 4 sin^{3} (u)

Factor

3 sin (u) - 4 sin^{3} (u) : sin (u) (3 - 4 sin^{2} (u))

= (3 - 4 sin^{2} (u)) sin (u)

= sin (u) (3 - 4 sin^{2} (u))

We showed that the two sides could take the same form

\Rightarrow True

2 cos^{2} (\frac{x}{2}) = 1 + cos (x)

tan (a) + \frac{cos ( a )}{1 + sin ( a )} = sec (a)

\frac{cos ^{2} ( A )}{cos ( A ) - sin ( A )} + \frac{sin ( A )}{1 - cot ( A )} = sin (A) + cos (A)

sec (a) + tan (a) = \frac{cos ( a )}{1 - sin ( a )}

cos (x - \frac{π}{6}) - sin (x + \frac{π}{3}) = 0

Is sin(3u)=sin(u)(3-4sin^2(u)) ?
The answer to whether sin(3u)=sin(u)(3-4sin^2(u)) is True